Here is the opening paragraph "Beer Engine's refractometer calculator approximates specific gravity from refractometer readings. Approximate is stressed because there is not a direct correlation between hydrometer readings and refractometer readings when measuring brewers' wort and the disparity is even worse once fermentation is under way. There are many contrary issues which make it difficult to use a refractometer accurately for brewing, particularly if trying to relate refractometer readings to specific gravity"
You are correct in saying a hydrometer needs to be calibrated to water but the point of calibrating the R to the H is the point GW makes above i.e. you are not using instruments that are capable of doing exactly the same job, they are not equivalents. Each wort composition is going to have a slightly different refractive index because wort is not a simple sucrose based solution which is what a R is designed to measure. Wort is nainly maltose, not sucrose and other complex sugars which change as your malt bill changes between recipes. On the same "page" you will find a calibration option so you can recalibrate the R to reflect the measuremnt the H is giving you. It basically calculates a conversion figure which once saved will ensure that the R now measures the same wort the same way as the H and will convert the Brix reading to SG. Most R's do have both scales but this is a bit of licence on the part of the manufacturer and only helps reinforce the incorrect notion that they are capable of being "exact" equivalents.
A further problem is that hot wort is also a problem for a hydrometer as they are typically calibrated to 20c and the higher the temperature the more inaccurate the temperature adjustment calculators become. The way I aproach these problems is to allow a trial jar of wort to cool to approx 20c then make the calibration adjustment on the refractometer in order to closely (and quickly) establish what the SG of the run off is so I don't start extracting tannins. Tasting the run off is another way, and you might think a lot simpler
